Official Journal of the Japan Wood Research Society
Table 5 Calculation of connection numbers for A1 and A2
From: Quantitative safety evaluation of ancient Chinese timber arch lounge bridges
| Â | Grade 1 | Grade 2 | Grade 3 | Grade 4 | Grade 5 | |||||
|---|---|---|---|---|---|---|---|---|---|---|
\(\mu_{i1} (w_{i1})\) | \(\mu_{i1}\) × \(w_{i1}\) | \(\mu_{i2}\)(\(w_{i2}\)) | \(\mu_{i2}\) × \(w_{i2}\) | \(\mu_{i3}\)(\(w_{i3}\)) | \(\mu_{i3}\) × \(w_{i3}\) | \(\mu_{i4}\)(\(w_{i4}\)) | \(\mu_{i4}\) × \(w_{i4}\) | \(\mu_{i5}\)(\(w_{i5}\)) | \(\mu_{i5}\) × \(w_{i5}\) | |
A1 | ||||||||||
 b1 | − 0.85 (0.049) | − 0.041 | 1.00 (0.042) | 0.042 | 0.85 (0.040) | 0.034 | − 1.00 (0.063) | − 0.063 | − 1.00 (0.033) | − 0.033 |
 b2 | − 1.00 (0.074) | − 0.074 | − 1.00 (0.074) | − 0.074 | 0.2 (0.084) | 0.017 | 1.00 (0.120) | 0.12 | − 0.2 (0.083) | − 0.017 |
 b3 | − 1.00 (0.509) | − 0.509 | − 1.00 (0.507) | − 0.507 | − 1.00 (0.519) | − 0.519 | − 0.20 (0.396) | − 0.079 | 1.00 (0.340) | 0.34 |
 b4 | − 1.00 (0.098) | − 0.098 | − 1.00 (0.130) | − 0.13 | − 0.50 (0.111) | − 0.056 | 1.00 (0.127) | 0.127 | 0.50 (0.175) | 0.088 |
 b5 | − 1.00 (0.061) | − 0.061 | − 1.00 (0.081) | − 0.081 | − 1.00 (0.104) | − 0.104 | 0.92 (0.158) | 0.146 | 1.00 (0.136) | 0.136 |
 b6 | − 1.00 (0.209) | − 0.209 | − 1.00 (0.166) | − 0.167 | − 0.84 (0.142) | − 0.12 | 1.00 (0.136) | 0.136 | 0.84 (0.233) | 0.196 |
 SUM | – | − 0.993 | – | − 0.917 | – | − 0.747 | – | 0.386 | – | 0.711 |
A2 | ||||||||||
 b1 | − 1.00 (0.068) | − 0.068 | − 0.09 (0.057) | − 0.005 | 1.00 (0.055) | 0.055 | 0.09 (0.086) | 0.008 | − 1.00 (0.044) | − 0.044 |
 b2 | − 1.00 (0.073) | − 0.073 | − 1.00 (0.072) | − 0.072 | − 0.20 (0.083) | − 0.017 | 1.00 (0.116) | 0.116 | 0.20 (0.080) | 0.016 |
 b3 | − 1.00 (0.475) | − 0.475 | − 1.00 (0.469) | − 0.469 | − 1.00 (0.483) | − 0.483 | − 0.20 (0.360) | − 0.072 | 1.00 (0.310) | 0.310 |
 b4 | − 1.00 (0.127) | − 0.127 | − 1.00 (0.167) | − 0.167 | − 1.00 (0.144) | − 0.144 | 0.67 (0.161) | 0.107 | 1.00 (0.221) | 0.221 |
 b5 | − 1.00 (0.061) | − 0.061 | − 1.00 (0.080) | − 0.080 | − 1.00 (0.103) | − 0.103 | 0.87 (0.154) | 0.134 | 1.00 (0.133) | 0.133 |
 b6 | − 1.00 (0.196) | − 0.196 | − 1.00 (0.154) | − 0.154 | − 0.84 (0.132) | − 0.111 | 1.00 (0.123) | 0.123 | 0.84 (0.212) | 0.178 |
 SUM | – | − 1.000 | – | − 0.948 | – | − 0.802 | – | 0.416 | – | 0.814 |